As written in the Arch wiki (link), by default, only root can change the brightness by this method. To allow users in the video group to change the brightness, a udev rule such as the following can be used (replace the <vendor> with your vendor id. E.g. acpi_video0, intel_backlight) :
% cat /etc/udev/rules.d/backlight.rules
ACTION=="add", SUBSYSTEM=="backlight", KERNEL=="<vendor>", RUN+="/bin/chgrp video /sys/class/backlight/%k/brightness"
ACTION=="add", SUBSYSTEM=="backlight", KERNEL=="<vendor>", RUN+="/bin/chmod g+w /sys/class/backlight/%k/brightness"
Then you need to add your user to the video group.
usermod -aG video <user>
After that this should work:
echo 5 > /sys/class/backlight/<vendor>/brightness